APPLICATIONS OF BAYESIAN METHODS TO THE PREDICTION OF EDUCATIONAL PERFORMANCE 1

The feasibility and effectiveness of a Bayesian method, due to Lindley, for estimating regressions in m groups is studied by application of the method to data from the Basic Research Service of The American College Testing Program. Evidence is found to support the belief that in many testing applications the collateral information obtained from each subset of m ‐ 1 colleges will be useful for the estimation of the regression in the m th college. Specifically, on cross‐validation in a second sample, the Bayesian predictions had a smaller mean squared error in each of the 22 colleges, the reduction averaging 9.7%, when compared with the least squares predictions when four predictor variables were used on a quarter sample in 22 colleges with initial within‐college sample sizes ranging from 26 to 184. Furthermore, even when based on the full sample within each college, the least squares predictions had an average cross‐validated mean squared error only barely less than the Bayesian predictions based on the quarter sample. The most apparent benefit of the Bayesian method is that it permits regression to be done in subpopulations (e.g., male‐female) where sample sizes are small and where the regressions are different in the subpopulations. In the present study a decrease of more than 10% in mean squared error was obtained using this approach.